行星轮系渐开线变位齿轮时变啮合刚度数值计算

Numerical Calculation of Planetary Gear Train Involute Modified Gear Time-Varying Meshing Stiffness

齿轮啮合刚度的时变性是齿轮产生振动的主要原因,对齿轮时变刚度进行求解计算具有重要的意义。基于正变位行星轮系外齿轮齿形几何参数的计算方法,根据内外齿轮齿形的不同,推导出内齿轮齿形几何参数计算过程。利用石川公式中轮齿变形计算公式和刚度求解公式,通过Matlab编程求得正变位行星轮系内外啮合时变啮合刚度曲线,并与Weber能量法计算结果进行对比,结果表明:静态刚度最大误差为3.7%,不考虑幅值为很小值时的动态刚度,前4阶谐波幅值最大误差约为9.1%,精度满足要求,可以为行星轮系运动微分方程提供较为准确的啮合刚度。

The time-varying gear meshing stiffness is the main cause of gear vibration. To caculate the time-varying meshing stiffness has vital significance. Based on geometric parameters calculation method of external gear tooth profile in positive modified planetary gear train,according to the differences between external and internal gear tooth profiles,the geometric parameters calculation method of internal gear tooth profile was deduced in detail. Using Ishikawa tooth deformation calculation formula and stiffness calculation formula,positive modified planetary gear train internaland external time-varying meshing stiffness curves can be got by Matlab programming. Compared with the calculation result of Weber energy method,maximum static stiffness error is 3. 7% and the first four order harmonic amplitude maximum error is 9. 1% without considering the small amplitude value of the dynamic stiffness. Calculation accuracy meets the requirements. It can provide relatively accurate meshing stiffness for motion differential equation of the planetary gear train.